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In short -- for tournaments, yes.
I never played with forced jumps as a kid, but my father-in-law always plays with forced jumps. So I did a little digging around, and this is what I found:
The American Checker Federation seems to be the only sanctioned checkers organization I could find. According to the American Checker Federation, rule #1.20 says
...

According to the American Checker Federation (see rule 12), a tie game is called a draw. The conditions for a draw are similar to the 50-move rule in chess. Basically, one player asks the other to prove he can win (or get closer to winning) in the next 40 moves or the game ends in a draw. I imagine this would only really occur in high level play, perhaps ...

From the Wikipedia article on checkers:
If a player's piece jumps into the kings row, the current move terminates; having just been crowned, the piece cannot continue on by jumping back out (as in a multiple jump), until the next move.

As per the the Official FMJD Rules for International Draughts, if the opponent notices that you have not captured as many pieces as possible, they may decide whether the move stands or if it must be taken back and made again.
5.4. If a player has committed one of the following irregularities, his opponent has the right to decide whether that irregularity ...

As was indicated by @JaysonSmith, a king can always be jumped by another king. This holds for any variant of draughts/checkers.
The privileges that a king obtains differ by variant, however.
backward movement: in all variants, kings can move backward, but men cannot.
backward capture: in all variants, kings can jump backward, but men cannot for ...

There are many variants of checkers/draughts, and for most of them (including the Checkers variant played predominantly in the English-speaking world), promotion is both mandatory and ending the move. Quote from the American Checkers Federation's official rulebook:
1.16 When a man reaches the farthest row forward (known as the “king-row” or ...

I am not a lawyer, and have experience only in Ontario, but under Ontario law wagering on games of skill is not gambling. In a well-known case from the 1960's or early 1970's, in which the St. Clair Bridge Studio was defending itself against charges of running a gambling house, barrister and bridge player Eric Murray in his winning defence argued that bridge ...

This depends on the variation you're playing. A lot of variations allow capturing backwards with regular pieces (called men). The English variation is probably the most common that doesn't allow backwards capturing. By the international rules, capturing backwards is allowed (and mandatory if it results in the largest capture group).
There's an extensive ...

It depends on if you are playing with mandatory capture rules or not. If you are playing with mandatory capture and they make a move instead of capturing a piece then you should tell them because they would be required to make the capture instead of another move. If you are not playing with mandatory capture then it doesn't matter but you can still tell them ...

(Warning: Clicking on the rulebook link below will download a Word document.)
From the American Checkers Federation's official rulebook (emphasis mine):
1.16 When a man reaches the farthest row forward (known as the “king-row” or “crown-head”) it becomes a king, and this completes the turn of play. The man can be crowned by either player ( ) by placing ...

All capturing moves are compulsory (with the exception of your choice of which capturing sequence to take).
It is a special case that causes a pieces movement to end when it is promoted.
In your case, the piece was already promoted before re-entering the king-row as part of a capturing sequence. Its movement does not end and you must continue to make the ...

No, on an 8x8 board and the regular American checkers rules, you can capture at most 9 out of the 12 pieces:
The white king can capture here the sequence (in chess notation)
h8 x f6 x h4 x f2 x d4 x b6 x d8 x f6 x d4 x b2
Note that the white king passes the squares f6 and d4 multiple times, which is allowed (what is not allowed, is jumping the same ...

Checkers is defintely not just tactics! While checkers is not in the same strategic league as chess, there are clear strategic concepts. For example, controlling the long diagonal is somewhat similar to the idea of controlling the centre in chess.
Another example is playing to open one side, for the purposes of crowning pieces. This is analogous to the idea ...

The answer by @RemcoGerlich is essentially correct. Some extra info below. For further reference see the Dutch book Drie tegen een is gemeen, that contains a mathematical proof that 3 vs. 1 kings is a draw (which predates the age of perfect knowledge endgame databases by almost a decade!).
The answer depends crucially on both the board geometry and the king ...

3 kings vs 1 king is usually not enough for force a win, because (as you discovered), you can't catch a king that can safely stay on the main diagonal.
The rules say that 1 king vs 1 king (where neither king is immediately lost) is an immediate draw; 2 kings (or a king and a piece) vs 1 king is a draw if no captures occur within five moves, three kings (or ...

Yes, a kinged-piece can certainly jump another kinged-piece. In fact, having a kinged-piece does NOT make it invulnerable to being 'jump'. This means that even a NON-kinged-piece can jump a kinged-piece. The only advantage to kinging a piece is that it is able to move both Forward and Backward. A non-kinged-piece can be severely limited in jumping due to ...

For American checkers on an 8x8 board, it is possible to get 24 kings on the board from the initial position. Here is a Java applet with a proof game of 211 moves.
For International draughts on a 10x10 board, it is possible to get 40 kings on the board from the initial position. Here is a Java applet with a proof game of 389 moves.

No, the game does not become unplayable.
Years ago, I regularly played without the forced capture rule, and found the experience enjoyable.
There is also have the Huffing Rule variant, where the capture is not forced, but by not taking the capture you lose that piece after your turn.

If your opponent is remarkably cooperative, you could, theoretically, get 12 kings on the board for your color.
Your opponent needs to open paths for you to get their back row in such a manner that you either do not get captured or can capture him on the way in.
I've had as many 8 in a game a couple times playing against a very not good opponent.

If you do not force capture then it's very possible, trivial even, to have a stalemate.
Even without though:
From wikipedia:
English draughts (American 8×8 checkers) has been the arena for several notable advances in game artificial intelligence. In the 1950s, Arthur Samuel created one of the first board game-playing programs of any kind. More recently, ...

There are many variants of checkers/draughts, and for all of them (including the Checkers variant played predominantly in the English-speaking world), not only is jumping compulsory, it is also compulsory to keep jumping until all the jumps are completed. Quote from the American Checkers Federation's official rulebook:
1.19 If a jump creates an ...

As Wikipedia already details, there are many different draughts variants, but there are two common rules and one exotic rule according to which kings can capture.
Long-ranged kings. This is the most common rule, which applies to e.g. the International/Brazilian/Canadian, Russian, Spanish and Czech draughts variants and to Pool checkers in the USA. A king ...

Yes, a king can do that, but he has to land in between two pieces. If the diagonal had been b - - w w - - -, he wouldn't have been able to capture the pieces.
And yes, a king can change direction, but again, he has to land on the field where he changes direction. A player must capture as many pieces as possible.
There are many variants of draughts, as ...

This depends on the exact variant of checkers you're talking about. In the primary version played in the US, the forced capture rule says that you must make captures if possible, but lets the player arbitrarily choose between capturing moves (emphasis mine):
1.20 All capturing moves are compulsory, whether offered actively or passively. If there are two ...

It depends on the checkers/draughts variant that you are playing:
For American checkers / Britisch draughts (which are two names for the same game) and Italian checkers, kings are short-ranged and cannot jump over empty squares.
For all other variants (International/Russian/Spanish/Czech/Frisian/Thai draughts and Pool checkers), kings are long-ranged and ...

The variant of checkers described here is most likely Pool Checkers, or is at least closely related. A quick Google search showed several online play sites along with general strategy write-ups. There is even an iPad app with VS Computer play.
Having never played the variant myself, I cannot give any specific advice on gameplay improvements.